Tunable organic solvent nanofiltration in self-assembled membranes at the sub–1 nm scale

Organic solvent–stable membranes exhibiting strong selectivity and high permeance have the potential to transform energy utilization in chemical separation processes. A key goal is developing materials with uniform, well-defined pores at the 1-nm scale, with sizes that can be tuned in small increments with high fidelity. Here, we demonstrate a class of organic solvent–stable nanoporous membranes derived from self-assembled liquid crystal mesophases that display such characteristics and elucidate their transport properties. The transport-regulating dimensions are defined by the mesophase geometry and can be controlled in increments of ~0.1 nm by modifying the chemical structure of the mesogen or the composition of the mesophase. The highly ordered nanostructure affords previously unidentified opportunities for the systematic design of organic solvent nanofiltration membranes with tailored selectivity and permeability and for understanding and modeling rejection in nanoscale flows. Hence, these membranes represent progress toward the goal of enabling precise organic solvent nanofiltration.

Section S1. Calculations of the limiting dimensions HI nanofiltration membranes function by an ordered array of hexagonally close-packed nanofibrils with well-defined center-to-center spacings from d = 3.1 to 3.9-nm. The prior study suggests the swelling by water is negligible. Here because the polymeric nanostructures from lyotropic self-assembled mesophases were cross-linked and anchored by covalent bonds, we assume the influence of solvent swelling is negligible. The solvent continuous nanochannel schematic listing the nomenclature of the geometric parameters is shown in Figure S5 below. Note the dissociation of the counterion Brfrom NH4Br depends on the solution dielectric constant, ε. Hence, the dissociated Brmay be presented as a part of the solvent continuum in aqueous solutions; alternatively, a larger diameter cylinder can be expected if there is no ionic dissociation. In turn, 2 cylinder volume fractions for each mesophase are approximated. The limiting dimension is derived from the below calculations:

Hydraulic Permeance Calculation
For ordered cylinders with low Reynolds fluid flow perpendicular to the long axis, the dimensionless hydraulic permeability = * of can be approximated as a function of solid volume fraction (45), Similarly, the dimensionless hydraulic permeability ‖ * of fluid flow parallel to the square array of fibers is (46): These calculations lead to the Darcy permeability from the dimensionless permeability factor * derived above.
From the above correlation, the hydraulic permeability P is estimated by accounting for the water viscosity μ that is 0.0011 Pa•s at 16°C: Where the P is directly related to the hydraulic permeance by factors of membrane thickness δ and tortuosity τ, When there are mixed cylinder orientations (i.e., parallel cylinders followed with perpendicular cylinders) across the membrane cross-section, the associated hydraulic permeance Lp is estimated with flow units in series,

The Calculation for Transport Characterization
The observed solute rejection Ro was directly calculated by comparing the solute concentration of the permeate to the feed. In the equation below, Cp is the permeate concentration, and Cf is the feed concentration, In the aqueous solution rejection (PEG) experiment, the intrinsic solute rejection Ra most accurately reflects the nanochannel sieving property. It was calculated by correlating the observed rejection of the effect of concentration polarization by an equation of the volumetric water flux Jw to the mass transfer coefficient k.
Since the Jw/k are always smaller than 0.3, there was no severe concentration polarization in aqueous solution experiments (47).
The concentration polarization correction was between 0.3 to 3% through the entire PEG rejection experiment. The mass transfer coefficient is estimated based on the Colton-Smith empirical correlation defined by a function of projected stir bar radius r, solute diffusion coefficient Di, solvent kinematic viscosity v, and the rotational speed ω of the magnetic stirring bar, Here, the Di values for polyethylene oxide molecules are retrieved from the literature. For other solutes, the Di is approximated using the Stoke-Einstein equation, = 6 (S. 16) In order to describe the rejection profile of HI templated membranes, a logistic function is employed to fit the sigmoidal-like progression of the molecular weight cut-off curve. By corresponding the solute diameter estimated from the Chem3D software package to the observed rejection, the fitting parameters β and γ best describing the rejection profile were derived (56),

Fig. S1. Polarized optical micrographs (POM) displaying the high-fidelity retention of the mesophase textures.
Micrographs were taken before and after the photo-induced polymerization for n5t, n6t, n6d, and n7d in thin-film. 20 wt.% mesophase solutions were spin-coated on pre-cleaned glass slides to prepare ~ 500 nm thick films. Consistent liquid crystal textures were observed without the emergence of optical inhomogeneities in the developed birefringence domains. Gel samples were prepared from ~20 wt.% solutions.    The bromide ion is assumed to dissociate from the fibril matrix in solvent with a high dielectric constant or bind with the matrix in solvent with a low dielectric constant, and hence the different volume fractions. The grey particle represents the limiting dimension available for solvent flow along the axial direction, and the green particle is the confining dimension in case of the solvent flow perpendicular to the cylinders.          Membrane performance is listed along with literature data. Here the self-assembled membranes stand out with superior solvent permeability relative to amorphous materials at high solute rejections. Error bars correspond to 95% confidence interval from multiple measurements.